I've gone on several weekend cabin getaways with women friends. What has worked for us is for each of us to choose a meal, and provide for everyone for that meal. We all help the cook, as needed, but the one person is responsible for planning, bringing supplies, and putting the meal on the table. Then you would get about 3 meals "off" while someone else is in charge.
One of the women in my group is super organized and puts an Excel spreadsheet together listing all the meals that need to be covered, along with drinks/snacks, and then posts it on Google and we all go fill in what we want to contribute.
I remember one other camping trip with several families, where two of the women took charge of the menus and did the shopping and then we chipped in our share of money. I was not pleased with this, as they bought WAY too much food, we didn't eat as much as the other families, and so I felt we paid more than our share and more than necessary for food for the trip.
Try to keep things as simple as possible. Does everyone really need three full meals every day? Or is it fine to have sandwich makings handy for a quick lunch, or simple breakfast foods that don't require cooking. Maybe plan just a few meals as group meals, and the rest are do as you please.